In this dissertation, the concept of Hopf-Galois extension that can be viewed as a principle bundle will be generalized to the concept of coalgebra Galois extension. It is shown that every coalgebra Galois extension induce a unique entwining map compatible with the right coactions. The existence of entwining map for every coalgebra Galois extension, lets us to relate the concept of coalgebra extensions to the concept of coalgebra principle bundle. Moreover, the dual notion of coalgebra Galois extension is defined and the analogous results are derived.
